Let's solve the equation:

\[
x^2 \cdot 8 = x^3
\]

### Step 1: Simplify the equation
First, divide both sides by \(x^2\) (assuming \(x \neq 0\)) to simplify:

\[
8 = x
\]

### Step 2: Verify the solution
Substitute \(x = 8\) back into the original equation to verify:

\[
8^2 \cdot 8 = 8^3
\]

Simplifying both sides:

\[
64 \cdot 8 = 512 \quad \text{and} \quad 8^3 = 512
\]

Both sides are equal, so the solution \(x = 8\) is correct.

### Final Answer:
The solution is \(x = 8\).

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Solve \(x^3 \cdot 4 = x^4\).
2. If \(5x^2 = x^3\), what is the value of \(x\)?
3. Solve the equation \(x^2 \cdot 10 = x^4\).
4. What is the solution to \(2x^2 = x^3\)?
5. If \(x^2 \cdot 7 = x^3 \cdot 2\), find \(x\).

**Tip:** When solving equations with variable exponents, look for ways to factor or simplify by dividing through by the lowest power of the variable.

Learn how to solve the exponential equation x^2 * 8 = x^3 with a detailed step-by-step solution. This problem covers key algebraic concepts, including exponential equations and simplification techniques. Suitable for students in Grades 10-12.

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